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Populate subscripts in homotopy analysis of equation of motion?

Posted 1 year ago
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Hello, I am seeking to Automate a code by populating subscript k in my equation of Motion. I define phi as a summation being u0+pu1+p^2u2+p^3u3.... and so on. I then define the conditional statement for phi being of value 0 when k is less than or equal to 1 and 1 if k is greater than 1. I then proceed to define the equation of motion for a simple duffing system evaluated with the Homotopy Analysis Method. The governing equation is dependent upon the value of k. k is the order of the Homotopy Analysis Method (HAM). I wanted to tell mathematica to symbolically evaluate the equation for a specific value of k, say 2 or 3. However when i did this the error message "Incomplete expression; more input is needed." came up. Please advise. Thank You enter image description here

HAM Automated Duffing Symbolic
Defining Phi

\[CurlyTheta] = \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(k = 0\), \(10\)]\(\((
\(\*SubscriptBox[\(u\), \(k\)]\)[\[Tau]])\)*\((
\*SuperscriptBox[\(p\), \(k\)])\)\)\);
Defining Chi
\[Chi][k_] := If[k <= 1, 0*k, k/k];
Defining HAM Equation for kth Order
Subscript[u, k][\[Tau]]'' + \[CapitalOmega]^2*
    Subscript[u, k][\[Tau]] == \[Chi][
     k]*(Subscript[u, k - 1][\[Tau]]'' + \[CapitalOmega]^2*
       Subscript[u, k - 1][\[Tau]]) + 
    0]*(1/(k - 
\[Tau])(D[\[CurlyTheta], {p, k - 1}] /. p \[RightArrow] 0)) + 
        2*c*((\[PartialD]/\[PartialD]\[Tau])(D[\[CurlyTheta], {p, 
               k - 1}] /. 
             p \[RightArrow] 0)) + \[Omega]^2*(D[\[CurlyTheta], {p, 
             k - 1}] /. 
           p \[RightArrow] 
            0) + \[Mu]*(D[\[CurlyTheta]^3, {p, k - 1}] /. 
           p \[RightArrow] 0) - 
        F*(D[Cos[\[CapitalOmega]*\[Tau]], p, k - 1] /. 
% /. {k\[LongRightArrow]1}
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